A central problem in Operations Research (OR) is optimization over time and under uncertainty. Proposed almost fifty years ago, dynamic programming (DP) is still considered the method of choice for such problems. However, even for very moderate dimensions, DP fails due to what Richard Bellman called ``the curse of dimensionality.'' Despite its genuine practical importance, it is fair to say that OR does not have a tractable, general theory for solving stochastic and dynamic optimization problems.

In this talk, I outline a proposal for such a theory. Motivated from practice, and approximate in nature, our proposal utilizes continuous linear programming as the central methodological tool enhanced by ideas in the approximate dynamic programming literature. We present analytical and computational evidence of successful application of this theory in several real world environments: revenue management, job shop scheduling, resource allocation in parallel computing, and routing in communication networks.